Special perturbations of rotating isothermal gas clouds with constant rotational velocity

A class of special perturbations of stationary rotating and self-gravitating gaseous clouds with constant rotational velocity and constant temperature is studied. The perturbations are isothermal and are connected with displacements only in the direction of the rotation axis. The author presents a perturbation equation which can be separated. The radial dependence of the perturbed variables is a simple closed expression, the angular dependence is given by an ordinary second order differential equation. The perturbed configurations show the asymptotic features of the regular solutions of the isothermal gas sphere. The relevance for the stability of the equilibrium state is discussed, and applications to the formation of the planetary system are considered.